Abstract

For a variety of UV optical coatings, surface roughness was measured by use of an atomic-force microscope (AFM) to study its dependence on the film material and thickness, coating design, and deposition process. After analyzing the corresponding power spectral density functions, we propose a simple classification model for coatings according to the contributions of substrate roughness and intrinsic film roughness to the scattering. Results of scattering measurements on different types of coatings are presented and are found to be in good agreement with predictions based on the AFM data. Consequences for a scatter reduction strategy are discussed.

© 1998 Optical Society of America

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    [CrossRef]
  2. J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
    [CrossRef]
  3. P. Bousquet, F. Flory, P. Roche, “Scattering from multilayer thin films: theory and experiment,” J. Opt. Soc. Am. 71, 1115–1123 (1981).
    [CrossRef]
  4. P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
    [CrossRef]
  5. J. M. Bennett, J. H. Dancy, “Stylus profiling instrument for measuring statistical properties of smooth optical surfaces,” Appl. Opt. 20, 1785–1802 (1981).
    [CrossRef] [PubMed]
  6. G. Rasigni, F. Varnier, M. Rasigni, P. Palmari, A. Llebaria, “Autocovariance functions for polished optical surfaces,” J. Opt. Soc. Am. 73, 222–233 (1983).
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  7. A. Duparré, “Effect of film thickness and interface roughness correlation on the light scattering from amorphous and from columnar structured optical films,” J. Mod. Opt. 38, 2413–2421 (1991).
    [CrossRef]
  8. J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
    [CrossRef] [PubMed]
  9. A. Duparré, H.-G. Walther, “Surface smoothing and roughening by dielectric thin film deposition,” Appl. Opt. 27, 1393–1395 (1988).
    [CrossRef]
  10. A. Duparré, A. Kiesel, S. Gliech, “Optical scattering and surface microstructure of thin films for laser application,” Rev. Laser Eng. Jpn. 24, 220–228 (1996).
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    [CrossRef]
  12. C. F. Hickey, C. Amra, E. Pelletier, “Scattering study of single layer titania films,” Appl. Opt. 28, 2754–2761 (1989).
    [CrossRef] [PubMed]
  13. C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).
    [CrossRef]
  14. D. Rönnow, “Elastic light scattering by thin films. Spectroscopic measurements and analysis,” Acta Univ. Ups. 208, 40–51 (1996).
  15. A. Duparré, S. Jakobs, “Combination of surface characterization techniques for investigating optical thin-film components,” Appl. Opt. 35, 5052–5058 (1996).
    [CrossRef]
  16. A. Duparré, “Light scattering of thin dielectric films,” in Thin Films for Optical Coatings, R. E. Hummel, K. H. Günther, eds., Vol. 1 of Handbook of Optical Properties Series (CRC, Boca Raton, Fla., 1995), pp. 273–304.
  17. C. Deumié, R. Richier, P. Dumas, C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
    [CrossRef]
  18. C. Ruppe, A. Duparré, “Roughness analysis of optical films and substrates by atomic force microscopy,” Thin Solid Films 288, 8–13 (1996).
    [CrossRef]
  19. W. M. Bruno, J. A. Roth, P. E. Burke, W. B. Hewitt, R. E. Holmbeck, D. G. Neal, “Prediction of the bidirectional reflectance-distribution function from atomic-force and scanning–tunneling microscope measurements of interfacial roughness,” Appl. Opt. 34, 1229–1238 (1995).
    [CrossRef] [PubMed]
  20. S. Jakobs, T. Feigl, A. Duparré, S. Pichlmaier, “Dependence of the surface morphology and scattering of optical coatings on film material, substrate roughness, and deposition process,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 196–206 (1996).
    [CrossRef]
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    [CrossRef]
  24. N. A. Burnham, R. J. Colton, H. M. Pollock, “Interpretation issues in force microscopy,” J. Vac. Sci. Technol. A 9, 2548–2556 (1991).
    [CrossRef]
  25. H. Truckenbrodt, A. Duparré, U. Schuhmann, “Roughness and defect characterization of optical surfaces by light scattering measurements,” in Specification and Measurement of Optical Systems, L. R. Baker, ed., Proc. SPIE1781, 139–151 (1992).
    [CrossRef]
  26. A. Duparré, S. Gliech, “Non-contact testing of optical surfaces by multiple-wavelength light scattering measurements,” in 10th Meeting on Optical Engineering in Israel, I. Shladov, Y. Weissman, eds., Proc. SPIE3110, 566–573 (1997).
    [CrossRef]
  27. J. C. Stover, Optical Scattering: Measurement and Analysis (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1995), pp. 77–81.
  28. A. Duparré, S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32, 5475–5480 (1993).
    [CrossRef]
  29. N. Kaiser, H. Uhlig, U. B. Schallenberg, B. Anton, U. Kaiser, K. Mann, E. Eva, “High damage threshold Al2O3/SiO2 dielectric coatings for excimer lasers,” Thin Solid Films 260, 86–92 (1995).
    [CrossRef]
  30. H. H. Bauer, M. Heller, N. Kaiser, “Optical coatings for uv photolithography systems,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 353–365 (1996).
    [CrossRef]
  31. B. A. Movchan, A. V. Demchishin, “Study of the structure and properties of thick vacuum condensates of nickel, titanium, tungsten, aluminium oxide and zirconium dioxide,” Phys. Met. Metalloved. (USSR) 8, 653–660 (1969).
  32. K. L. Westra, D. J. Thomson, “The microstructure of thin films observed using atomic force microscopy,” Thin Solid Films 257, 15–21 (1995).
    [CrossRef]
  33. K. H. Guenther, “Microstructure of vapor-deposited optical coatings,” Appl. Opt. 23, 3806–3815 (1984).
    [CrossRef] [PubMed]
  34. U. Kaiser, N. Kaiser, P. Weissbrodt, U. Mademann, E. Hacker, H. Müller, “Structure of thin fluoride films deposited on amorphous substrates,” Thin Solid Films 217, 7–16 (1992).
    [CrossRef]
  35. R. Thielsch, Fraunhofer Institute D-07745 Jena, Germany (personal communication, 1997).
  36. U. Schulz, S. Jakobs, N. Kaiser, “SiO2 protective coatings on plastic optics deposited with plasma IAD,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 169–174 (1996).
    [CrossRef]
  37. C. Amra, C. Grezes-Besset, P. Roche, E. Pelletier, “Description of a scattering apparatus: application to the problems of characterization of opaque surfaces,” Appl. Opt. 28, 2723–2730 (1989).
    [CrossRef] [PubMed]
  38. C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
    [CrossRef] [PubMed]
  39. E. L. Church, “Fractal surface finish,” Appl. Opt. 27, 1518–1526 (1988).
    [CrossRef] [PubMed]

1996

A. Duparré, A. Kiesel, S. Gliech, “Optical scattering and surface microstructure of thin films for laser application,” Rev. Laser Eng. Jpn. 24, 220–228 (1996).
[CrossRef]

D. Rönnow, “Elastic light scattering by thin films. Spectroscopic measurements and analysis,” Acta Univ. Ups. 208, 40–51 (1996).

A. Duparré, S. Jakobs, “Combination of surface characterization techniques for investigating optical thin-film components,” Appl. Opt. 35, 5052–5058 (1996).
[CrossRef]

C. Deumié, R. Richier, P. Dumas, C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
[CrossRef]

C. Ruppe, A. Duparré, “Roughness analysis of optical films and substrates by atomic force microscopy,” Thin Solid Films 288, 8–13 (1996).
[CrossRef]

1995

W. M. Bruno, J. A. Roth, P. E. Burke, W. B. Hewitt, R. E. Holmbeck, D. G. Neal, “Prediction of the bidirectional reflectance-distribution function from atomic-force and scanning–tunneling microscope measurements of interfacial roughness,” Appl. Opt. 34, 1229–1238 (1995).
[CrossRef] [PubMed]

N. Kaiser, H. Uhlig, U. B. Schallenberg, B. Anton, U. Kaiser, K. Mann, E. Eva, “High damage threshold Al2O3/SiO2 dielectric coatings for excimer lasers,” Thin Solid Films 260, 86–92 (1995).
[CrossRef]

K. L. Westra, D. J. Thomson, “The microstructure of thin films observed using atomic force microscopy,” Thin Solid Films 257, 15–21 (1995).
[CrossRef]

1994

1993

1992

U. Kaiser, N. Kaiser, P. Weissbrodt, U. Mademann, E. Hacker, H. Müller, “Structure of thin fluoride films deposited on amorphous substrates,” Thin Solid Films 217, 7–16 (1992).
[CrossRef]

C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[CrossRef] [PubMed]

1991

N. A. Burnham, R. J. Colton, H. M. Pollock, “Interpretation issues in force microscopy,” J. Vac. Sci. Technol. A 9, 2548–2556 (1991).
[CrossRef]

P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

A. Duparré, “Effect of film thickness and interface roughness correlation on the light scattering from amorphous and from columnar structured optical films,” J. Mod. Opt. 38, 2413–2421 (1991).
[CrossRef]

1989

1988

1984

1983

1981

1980

1979

J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116–124 (1979).
[CrossRef]

J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
[CrossRef]

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).
[CrossRef]

1969

B. A. Movchan, A. V. Demchishin, “Study of the structure and properties of thick vacuum condensates of nickel, titanium, tungsten, aluminium oxide and zirconium dioxide,” Phys. Met. Metalloved. (USSR) 8, 653–660 (1969).

Amra, C.

Anton, B.

N. Kaiser, H. Uhlig, U. B. Schallenberg, B. Anton, U. Kaiser, K. Mann, E. Eva, “High damage threshold Al2O3/SiO2 dielectric coatings for excimer lasers,” Thin Solid Films 260, 86–92 (1995).
[CrossRef]

Apfel, J. H.

Bauer, H. H.

H. H. Bauer, M. Heller, N. Kaiser, “Optical coatings for uv photolithography systems,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 353–365 (1996).
[CrossRef]

Bennett, J. M.

Bousquet, P.

Bruno, W. M.

Burke, P. E.

Burnham, N. A.

N. A. Burnham, R. J. Colton, H. M. Pollock, “Interpretation issues in force microscopy,” J. Vac. Sci. Technol. A 9, 2548–2556 (1991).
[CrossRef]

Bussemer, P.

P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

Carniglia, C. K.

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).
[CrossRef]

Church, E. L.

Colton, R. J.

N. A. Burnham, R. J. Colton, H. M. Pollock, “Interpretation issues in force microscopy,” J. Vac. Sci. Technol. A 9, 2548–2556 (1991).
[CrossRef]

Dancy, J. H.

Demchishin, A. V.

B. A. Movchan, A. V. Demchishin, “Study of the structure and properties of thick vacuum condensates of nickel, titanium, tungsten, aluminium oxide and zirconium dioxide,” Phys. Met. Metalloved. (USSR) 8, 653–660 (1969).

Deumié, C.

Dumas, P.

Duparré, A.

C. Ruppe, A. Duparré, “Roughness analysis of optical films and substrates by atomic force microscopy,” Thin Solid Films 288, 8–13 (1996).
[CrossRef]

A. Duparré, S. Jakobs, “Combination of surface characterization techniques for investigating optical thin-film components,” Appl. Opt. 35, 5052–5058 (1996).
[CrossRef]

A. Duparré, A. Kiesel, S. Gliech, “Optical scattering and surface microstructure of thin films for laser application,” Rev. Laser Eng. Jpn. 24, 220–228 (1996).
[CrossRef]

A. Duparré, S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32, 5475–5480 (1993).
[CrossRef]

A. Duparré, “Effect of film thickness and interface roughness correlation on the light scattering from amorphous and from columnar structured optical films,” J. Mod. Opt. 38, 2413–2421 (1991).
[CrossRef]

A. Duparré, H.-G. Walther, “Surface smoothing and roughening by dielectric thin film deposition,” Appl. Opt. 27, 1393–1395 (1988).
[CrossRef]

A. Duparré, “Light scattering of thin dielectric films,” in Thin Films for Optical Coatings, R. E. Hummel, K. H. Günther, eds., Vol. 1 of Handbook of Optical Properties Series (CRC, Boca Raton, Fla., 1995), pp. 273–304.

A. Duparré, S. Gliech, “Non-contact testing of optical surfaces by multiple-wavelength light scattering measurements,” in 10th Meeting on Optical Engineering in Israel, I. Shladov, Y. Weissman, eds., Proc. SPIE3110, 566–573 (1997).
[CrossRef]

H. Truckenbrodt, A. Duparré, U. Schuhmann, “Roughness and defect characterization of optical surfaces by light scattering measurements,” in Specification and Measurement of Optical Systems, L. R. Baker, ed., Proc. SPIE1781, 139–151 (1992).
[CrossRef]

S. Jakobs, T. Feigl, A. Duparré, S. Pichlmaier, “Dependence of the surface morphology and scattering of optical coatings on film material, substrate roughness, and deposition process,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 196–206 (1996).
[CrossRef]

Elson, J. M.

Eva, E.

N. Kaiser, H. Uhlig, U. B. Schallenberg, B. Anton, U. Kaiser, K. Mann, E. Eva, “High damage threshold Al2O3/SiO2 dielectric coatings for excimer lasers,” Thin Solid Films 260, 86–92 (1995).
[CrossRef]

Feigl, T.

S. Jakobs, T. Feigl, A. Duparré, S. Pichlmaier, “Dependence of the surface morphology and scattering of optical coatings on film material, substrate roughness, and deposition process,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 196–206 (1996).
[CrossRef]

Flory, F.

Gliech, S.

A. Duparré, A. Kiesel, S. Gliech, “Optical scattering and surface microstructure of thin films for laser application,” Rev. Laser Eng. Jpn. 24, 220–228 (1996).
[CrossRef]

A. Duparré, S. Gliech, “Non-contact testing of optical surfaces by multiple-wavelength light scattering measurements,” in 10th Meeting on Optical Engineering in Israel, I. Shladov, Y. Weissman, eds., Proc. SPIE3110, 566–573 (1997).
[CrossRef]

Grezes-Besset, C.

Guenther, K. H.

Hacker, E.

U. Kaiser, N. Kaiser, P. Weissbrodt, U. Mademann, E. Hacker, H. Müller, “Structure of thin fluoride films deposited on amorphous substrates,” Thin Solid Films 217, 7–16 (1992).
[CrossRef]

Hehl, K.

P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

Heller, M.

H. H. Bauer, M. Heller, N. Kaiser, “Optical coatings for uv photolithography systems,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 353–365 (1996).
[CrossRef]

Hewitt, W. B.

Hickey, C. F.

Holmbeck, R. E.

Jakobs, S.

A. Duparré, S. Jakobs, “Combination of surface characterization techniques for investigating optical thin-film components,” Appl. Opt. 35, 5052–5058 (1996).
[CrossRef]

S. Jakobs, T. Feigl, A. Duparré, S. Pichlmaier, “Dependence of the surface morphology and scattering of optical coatings on film material, substrate roughness, and deposition process,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 196–206 (1996).
[CrossRef]

U. Schulz, S. Jakobs, N. Kaiser, “SiO2 protective coatings on plastic optics deposited with plasma IAD,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 169–174 (1996).
[CrossRef]

Kaiser, N.

N. Kaiser, H. Uhlig, U. B. Schallenberg, B. Anton, U. Kaiser, K. Mann, E. Eva, “High damage threshold Al2O3/SiO2 dielectric coatings for excimer lasers,” Thin Solid Films 260, 86–92 (1995).
[CrossRef]

U. Kaiser, N. Kaiser, P. Weissbrodt, U. Mademann, E. Hacker, H. Müller, “Structure of thin fluoride films deposited on amorphous substrates,” Thin Solid Films 217, 7–16 (1992).
[CrossRef]

H. H. Bauer, M. Heller, N. Kaiser, “Optical coatings for uv photolithography systems,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 353–365 (1996).
[CrossRef]

U. Schulz, S. Jakobs, N. Kaiser, “SiO2 protective coatings on plastic optics deposited with plasma IAD,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 169–174 (1996).
[CrossRef]

Kaiser, U.

N. Kaiser, H. Uhlig, U. B. Schallenberg, B. Anton, U. Kaiser, K. Mann, E. Eva, “High damage threshold Al2O3/SiO2 dielectric coatings for excimer lasers,” Thin Solid Films 260, 86–92 (1995).
[CrossRef]

U. Kaiser, N. Kaiser, P. Weissbrodt, U. Mademann, E. Hacker, H. Müller, “Structure of thin fluoride films deposited on amorphous substrates,” Thin Solid Films 217, 7–16 (1992).
[CrossRef]

Kassam, S.

A. Duparré, S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32, 5475–5480 (1993).
[CrossRef]

P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

Kiesel, A.

A. Duparré, A. Kiesel, S. Gliech, “Optical scattering and surface microstructure of thin films for laser application,” Rev. Laser Eng. Jpn. 24, 220–228 (1996).
[CrossRef]

Llebaria, A.

Mademann, U.

U. Kaiser, N. Kaiser, P. Weissbrodt, U. Mademann, E. Hacker, H. Müller, “Structure of thin fluoride films deposited on amorphous substrates,” Thin Solid Films 217, 7–16 (1992).
[CrossRef]

Mann, K.

N. Kaiser, H. Uhlig, U. B. Schallenberg, B. Anton, U. Kaiser, K. Mann, E. Eva, “High damage threshold Al2O3/SiO2 dielectric coatings for excimer lasers,” Thin Solid Films 260, 86–92 (1995).
[CrossRef]

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), pp. 38–50.

Movchan, B. A.

B. A. Movchan, A. V. Demchishin, “Study of the structure and properties of thick vacuum condensates of nickel, titanium, tungsten, aluminium oxide and zirconium dioxide,” Phys. Met. Metalloved. (USSR) 8, 653–660 (1969).

Müller, H.

U. Kaiser, N. Kaiser, P. Weissbrodt, U. Mademann, E. Hacker, H. Müller, “Structure of thin fluoride films deposited on amorphous substrates,” Thin Solid Films 217, 7–16 (1992).
[CrossRef]

Neal, D. G.

Palmari, P.

Pelletier, E.

Pichlmaier, S.

S. Jakobs, T. Feigl, A. Duparré, S. Pichlmaier, “Dependence of the surface morphology and scattering of optical coatings on film material, substrate roughness, and deposition process,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 196–206 (1996).
[CrossRef]

Pollock, H. M.

N. A. Burnham, R. J. Colton, H. M. Pollock, “Interpretation issues in force microscopy,” J. Vac. Sci. Technol. A 9, 2548–2556 (1991).
[CrossRef]

Rahn, J. P.

Rasigni, G.

Rasigni, M.

Richier, R.

Roche, P.

Rönnow, D.

D. Rönnow, “Elastic light scattering by thin films. Spectroscopic measurements and analysis,” Acta Univ. Ups. 208, 40–51 (1996).

Roth, J. A.

Ruppe, C.

C. Ruppe, A. Duparré, “Roughness analysis of optical films and substrates by atomic force microscopy,” Thin Solid Films 288, 8–13 (1996).
[CrossRef]

Schallenberg, U. B.

N. Kaiser, H. Uhlig, U. B. Schallenberg, B. Anton, U. Kaiser, K. Mann, E. Eva, “High damage threshold Al2O3/SiO2 dielectric coatings for excimer lasers,” Thin Solid Films 260, 86–92 (1995).
[CrossRef]

Schuhmann, U.

H. Truckenbrodt, A. Duparré, U. Schuhmann, “Roughness and defect characterization of optical surfaces by light scattering measurements,” in Specification and Measurement of Optical Systems, L. R. Baker, ed., Proc. SPIE1781, 139–151 (1992).
[CrossRef]

Schulz, U.

U. Schulz, S. Jakobs, N. Kaiser, “SiO2 protective coatings on plastic optics deposited with plasma IAD,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 169–174 (1996).
[CrossRef]

Stover, J. C.

J. C. Stover, Optical Scattering: Measurement and Analysis (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1995), Chap. 2.
[CrossRef]

J. C. Stover, Optical Scattering: Measurement and Analysis (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1995), pp. 77–81.

Thielsch, R.

R. Thielsch, Fraunhofer Institute D-07745 Jena, Germany (personal communication, 1997).

Thomson, D. J.

K. L. Westra, D. J. Thomson, “The microstructure of thin films observed using atomic force microscopy,” Thin Solid Films 257, 15–21 (1995).
[CrossRef]

Truckenbrodt, H.

H. Truckenbrodt, A. Duparré, U. Schuhmann, “Roughness and defect characterization of optical surfaces by light scattering measurements,” in Specification and Measurement of Optical Systems, L. R. Baker, ed., Proc. SPIE1781, 139–151 (1992).
[CrossRef]

Uhlig, H.

N. Kaiser, H. Uhlig, U. B. Schallenberg, B. Anton, U. Kaiser, K. Mann, E. Eva, “High damage threshold Al2O3/SiO2 dielectric coatings for excimer lasers,” Thin Solid Films 260, 86–92 (1995).
[CrossRef]

Varnier, F.

Walther, H.-G.

Weissbrodt, P.

U. Kaiser, N. Kaiser, P. Weissbrodt, U. Mademann, E. Hacker, H. Müller, “Structure of thin fluoride films deposited on amorphous substrates,” Thin Solid Films 217, 7–16 (1992).
[CrossRef]

Westra, K. L.

K. L. Westra, D. J. Thomson, “The microstructure of thin films observed using atomic force microscopy,” Thin Solid Films 257, 15–21 (1995).
[CrossRef]

Acta Univ. Ups.

D. Rönnow, “Elastic light scattering by thin films. Spectroscopic measurements and analysis,” Acta Univ. Ups. 208, 40–51 (1996).

Appl. Opt.

A. Duparré, S. Jakobs, “Combination of surface characterization techniques for investigating optical thin-film components,” Appl. Opt. 35, 5052–5058 (1996).
[CrossRef]

C. F. Hickey, C. Amra, E. Pelletier, “Scattering study of single layer titania films,” Appl. Opt. 28, 2754–2761 (1989).
[CrossRef] [PubMed]

W. M. Bruno, J. A. Roth, P. E. Burke, W. B. Hewitt, R. E. Holmbeck, D. G. Neal, “Prediction of the bidirectional reflectance-distribution function from atomic-force and scanning–tunneling microscope measurements of interfacial roughness,” Appl. Opt. 34, 1229–1238 (1995).
[CrossRef] [PubMed]

J. M. Bennett, J. H. Dancy, “Stylus profiling instrument for measuring statistical properties of smooth optical surfaces,” Appl. Opt. 20, 1785–1802 (1981).
[CrossRef] [PubMed]

J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
[CrossRef] [PubMed]

A. Duparré, H.-G. Walther, “Surface smoothing and roughening by dielectric thin film deposition,” Appl. Opt. 27, 1393–1395 (1988).
[CrossRef]

C. Deumié, R. Richier, P. Dumas, C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
[CrossRef]

A. Duparré, S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32, 5475–5480 (1993).
[CrossRef]

K. H. Guenther, “Microstructure of vapor-deposited optical coatings,” Appl. Opt. 23, 3806–3815 (1984).
[CrossRef] [PubMed]

C. Amra, C. Grezes-Besset, P. Roche, E. Pelletier, “Description of a scattering apparatus: application to the problems of characterization of opaque surfaces,” Appl. Opt. 28, 2723–2730 (1989).
[CrossRef] [PubMed]

C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[CrossRef] [PubMed]

E. L. Church, “Fractal surface finish,” Appl. Opt. 27, 1518–1526 (1988).
[CrossRef] [PubMed]

J. Mod. Opt.

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Figures (22)

Fig. 1
Fig. 1

PSD curves of superpolished substrates (1, SP; and 2, Si wafer) calculated from AFM measurements over a scan area of 10 × 10 μm2. For spatial frequencies <1 μm-1, the curves are increased owing to scanner bow. Yet, this artificial increase remains below the surface roughness level of a conventionally polished QZ substrate (curve 3).

Fig. 2
Fig. 2

Spatial frequency bandwidth of AFM measurements and scattering bandwidths for different wavelengths. The dashed–line sections denote the frequency range in which, depending on the particular surface topography, AFM measurements may be distorted by scanner bow (low frequencies) or tip imaging (high frequencies). The scattering bandwidths correspond to a range of scattering angles from 2–84°.

Fig. 3
Fig. 3

PSD functions for substrates used in the experiments as calculated from AFM measurements. 1, superpolished SP; 2, superpolished Si wafer; 3, QZ; 4, SQ1; and 5, RG 1000.

Fig. 4
Fig. 4

AFM top-view images of Al2O3 single layers of different thicknesses deposited by EBD on SQ1. Left: Thickness 37 nm, gray scale ranges from 0 to 10 nm. Right: Thickness 965 nm, gray scale ranges from 0 to 10 nm.

Fig. 5
Fig. 5

AFM top-view images of LaF3 single layers of different thicknesses deposited by means of EBD on SQ1. Left: Thickness 37 nm, gray scale ranges from 0 to 10 nm. Right: Thickness 380 nm, gray scale ranges from 0 to 100 nm.

Fig. 6
Fig. 6

PSD functions of LaF3 single layers of different thicknesses deposited by means of electron-beam evaporation. The PSD of the pure substrate (SQ1) is added for comparison.

Fig. 7
Fig. 7

PSD functions of Al2O3 single layers of different thicknesses deposited by means of electron-beam evaporation. The PSD of the pure substrate (SQ1) has been added for comparison.

Fig. 8
Fig. 8

PSD functions of two substrates with different surface roughnesses (RG 1000 glass and Si wafer) and of LaF3 single layers (thickness 100 nm) deposited onto these substrates. The PSD functions of the layers coincide at spatial frequencies >10 μm-1.

Fig. 9
Fig. 9

PSD functions of Al2O3 single layers deposited by means of electron-beam evaporation onto RG 1000 with and without substrate heating (T s = 570 K; 300 K). The PSD curves of the layers coincide over the whole frequency range.

Fig. 10
Fig. 10

AFM top-view images of Al2O3 single layers deposited by means of IAD at different ion energies. Left: Ion energy 110 eV, σ = 0.95 nm. Right: Ion energy 150 eV. σ = 0.35 nm. Gray scales range from 0 to 10 nm.

Fig. 11
Fig. 11

PSD functions of Al2O3 single layers deposited by means of IAD at three different ion energies. The PSD of the pure substrate (SQ1) is added for comparison.

Fig. 12
Fig. 12

PSD functions of the top surface of reflective layer systems with different number of layers deposited by means of electron-beam evaporation onto RG 1000. S: RG 1000; H: quarter-wave layer Al2O3 (thickness 49 nm); L: quarter-wave layer SiO2 (thickness 55 nm).

Fig. 13
Fig. 13

AFM top-view images (10 × 10 μm2) of reflective layer systems with 49 layers deposited by means of electron-beam evaporation onto different substrates. Left: Layer system on RG 1000. Right: Layer system on superpolished SP. Gray scales range from 0 to 20 nm in both images.

Fig. 14
Fig. 14

PSD functions of HR oxide systems with 49 layers deposited by means of electron-beam evaporation onto different substrates. The PSD’s of the layer systems coincide at spatial frequencies >3 μm-1. The PSD’s of the pure substrates (superpolished SP and RG 1000) have been added for comparison.

Fig. 15
Fig. 15

Three-dimensional AFM images of fluoride layer systems consisting of different numbers of layers, deposited by means of electron-beam evaporation onto QZ. (a) QZ/2H 2L. (b) QZ/(2H 2L)8.

Fig. 16
Fig. 16

PSD functions of the top surface of fluoride layer systems consisting of different numbers of layers, deposited by means of electron-beam evaporation. S: crystalline quartz glass; 2H: half-wave layer LaF3 (thickness 100 nm); 2L: half-wave layer MgF2 (thickness 116 nm).

Fig. 17
Fig. 17

Schematic drawing of PSD curves and of the locations of characteristic frequencies for the proposed three types of surface roughness. f l S and f h S denote the high- and the low-frequency limits of the scattering bandwidth; f F is a frequency corresponding to the mean lateral diameter of the thin-film microstructure; and f SF denotes the frequency at which the substrate PSD intersects the PSD of the pure film. (a) total substrate replication, (b) partial substrate replication, and (c) thin-film dominance.

Fig. 18
Fig. 18

ARS (λ = 325 nm) of a superpolished Si wafer and of the single-, two-, and three-layer fluoride systems deposited onto Si wafer.

Fig. 19
Fig. 19

Measurement (solid curve) and calculation (dashed curve) of ARS for a Si wafer and the three-layer fluoride system deposited onto Si wafer.

Fig. 20
Fig. 20

ARS (λ = 325 nm) of an RG 1000 substrate and of the single- and the three-layer system of fluoride materials deposited onto RG 1000.

Fig. 21
Fig. 21

Measurement and calculation of ARS (λ = 325 nm) of the HR oxide system with 49 layers deposited onto RG 1000 (left) and superpolished SP (right).

Fig. 22
Fig. 22

Total backscattering measured over a lateral distance of 10 mm across the sample surface for the oxide HR system on superpolished SP (solid curve) and RG 1000 (dashed curve). λ = 325 nm.

Tables (5)

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Table 1 Overview of Coatings Investigated in This Study

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Table 2 Rms Roughness Values of an SQ1 Substrate and of Al2O3 and LaF3 Single Layers of Different Thicknesses Deposited onto SQ1

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Table 3 Rms Roughness Values of Superpolished SP and RG 1000 and of the 49-Layer Oxide System Deposited onto These Substrates

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Table 4 Classification of the Investigated Single Layers and Layer Systems According to the Contribution of the Substrate Roughness and Intrinsic Film Roughness to the PSD of the Top Surface Within the Scattering Bandwidth at λ = 325 nm

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Table 5 Comparison of Measured and Predicted Total Backscattering (λ = 325 nm) of the Oxide HR Coating on RG 1000 and Superpolished SP

Equations (7)

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σ=limL1L20L0Lhx, y2dydx1/2,
Sfx, fy=limL1L20L0L hx, yexp-j2πfxx+fyydxdy2.
fh=12πhR1/2,
1PidPSϑS, φSdΩ=16π2λ4cos ϑicos2 ϑSQϑS, φSSfx, fy,
fx=sin ϑScos φS-sin ϑiλ,
fy=sin ϑSsin φSλ.
S=PSPi.

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